CP from a Prior Race

One race you have already run tells you a lot about the power you could hold for longer or shorter. Give its average power and its finishing time, and a Riegel exponent for how quickly your sustainable power fades as an effort lengthens, and this projects the two together: CP = race power × (TTE ÷ race time)^e.

The exponent is a decay rate — it is the fraction of power you lose each time an effort doubles in length, about 2.7 % at −0.04 and 8.0 % at −0.12. How much it matters depends entirely on how far the projection reaches: for a 10 k finishing near your time to exhaustion it moves the answer by a few watts, and for a marathon by nearly forty.

The number this gives you is your power at a chosen duration — fifty minutes unless you say otherwise. That is not the same quantity as the critical power the two- and multi-effort calculators fit, which is the asymptote of a power-duration curve; the two differ by roughly W′ divided by that duration.